FIDE Championship odds after round three

6/26/2004 – The favorites are still the favorites, says Jeff Sonas. He has calculated the odds of each player in the sweet sixteen winning the event. Nakamura's 122 to 1 doesn't look so good, unless you placed your bet back when he was at 785 to 1! Plus, what is the best qualifying tournament system for a world championship?

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Place your bets

Although there have been plenty of high-rated casualties in the first three
rounds of the FIDE championship tournament in Tripoli, the two tournament favorites
have continued to advance. Going into the
previous round, #3 seed Michael Adams had pulled into a statistical
tie with #1 seed Veselin Topalov, with each player having a 16% chance to win
the tournament. This was partially because Topalov had a much tougher Round
3 opponent than did Adams. But by defeating Movsesian, Topalov has once again
pulled in front, with a 19% chance to win the tournament, compared to 17% for
Adams. Topalov's chances were also given a boost when #4 seed Vassily Ivanchuk,
a likely semifinal opponent, was eliminated. Here are the current odds for all
sixteen players, as of the end of Round 3:

I have been calculating these FIDE knockout tournament odds for years, going
back to Alexander Khalifman's win in Las Vegas in 1999. Back then, I was naively
trusting that the FIDE ratings were perfectly accurate. That led to some embarrassing
predictions over the years. Most memorable for me, due to the amount of nasty
emails I got during the tournament, was the fantastic performance by Alexander
Grischuk in 2000. He had a relatively low pre-tournament FIDE rating, and as
the tournament progressed, I kept calling him the heavy underdog each round,
ignoring the recent evidence of the tournament itself. And he kept winning,
and I kept getting email from Grischuk fans saying "I told you so!"
By the time the next FIDE championship tournament rolled around, I had learned
my lesson, and kept adjusting #19 seed Ruslan Ponomariov's "estimated strength"
higher and higher as he kept advancing through the tournament.

Similarly, the lower-rated players who are still in the Tripoli tournament
have shown clear evidence that they are underrated by the FIDE list. For instance,
before the tournament started, #83 seed Hikaru Nakamura looked to be at least
150 points weaker than #3 seed Michael Adams. By now it looks more like a 100-point
gap, based on Nakamura's apparent current form. Similarly, the estimated gap
in strength between #1 seed Veselin Topalov and #49 seed Zdenko Kozul was 100
points before the tournament, and now it's down to 70 points. I'm not saying
that the FIDE list will immediately show the gap closing so rapidly, because
I'm sure it won't. I'm talking more about my "best guess" statistical
estimate of each player's current strength. When we acknowledge that ratings
are not the super-accurate measurements we would like them to be, we have to
place less emphasis on the original rating list, and correspondingly more emphasis
on the recent evidence of the tournament results themselves. This is also what
we would witness if the rating mechanism were more dynamic.

Nevertheless, Topalov and Adams remain the clear favorites, even though their
Round 4 opponents have also done well thus far. There is a good reason why Topalov
and Adams are rated so high, and even giving Nakamura and Kozul considerable
credit for what they've done in the first three rounds, my calculations still
give Adams an 80% chance to eliminate Nakamura, and Topalov a 70% chance to
eliminate Kozul.

Knock-outs, good or evil?

While I have your attention, I would like to return to the general topic of
knockout tournaments, because I believe we can make substantial practical improvements
to the current format. Some of you may recall an article I wrote a couple of
years ago, as a follow-up to Yasser Seirawan's "Fresh Start" proposal
for unifying the world chess championship. In that article, I evaluated thousands
of different formats for determining the world champion, including various combinations
of knockout or Swiss or round-robin qualifying tournaments, followed by candidates
matches of various lengths. At the time, my conclusion was that FIDE's 128-player
knockout tournament was an extremely poor way to determine a world champion,
whereas Yasser's suggestion (a Swiss qualifier leading to a series of long candidate
matches) was in fact a fantastic way to determine a world champion. In fact,
it was almost the ideal format, mathematically speaking.

However, Yasser told me later that he was surprised by the negative reaction
from top players regarding his suggestion of a Swiss qualifier. But when you
think about it from a top player's perspective, it really makes sense. In a
Swiss tournament, or even a round-robin tournament, it is very difficult to
"force" your way into first place on your own. Almost invariably,
you need indirect help from the other players (who can either defeat your top
challengers or at least hold them to a draw). Because of this interdependence,
in such an important and lucrative event, it is inevitable that there will be
accusations of collusion: either an out-of-contention player not trying their
hardest, or two players agreeing to a mutually beneficial "grandmaster
draw".

According to Yasser, the top players much preferred the idea of a knockout,
where neither of those collusion scenarios is relevant. In a knockout, all players
are equally "in contention" until the moment they are eliminated,
so nobody would choose to intentionally lose a game, and even if they did, it
doesn't really hurt anyone else's chances very much. And two players in a knockout
might agree to a brief draw for short-term tactical reasons, but that will only
make their own match last even longer, to their own detriment in the long term.
So, from a sporting perspective, the knockout tournament is very appealing to
the top players, who feel more in control of their own destiny. Plus, knockouts
are simply more fun to follow. Every game matters.

Well, what's wrong with the knockout format? Easy: with so many participants,
and so little time, there is just not enough room to identify the single strongest
player in the field. It is very easy for the strongest player to falter in one
game and suddenly become eliminated. We expect that an effective championship
cycle will allow the strongest player (whoever that might be) a real chance
to demonstrate their superiority by winning the cycle, and this clearly isn't
the case when a minus-one score over a stretch of two games can eliminate you
from the whole cycle, however much success you had in the previous games during
the tournament.

Thus a knockout tournament should not be the final championship event, merely
a preliminary qualifying event. And there needs to be a way for a truly strong
player to lose a match and nevertheless ultimately qualify for the championship,
either through the use of a double-elimination format, or by there being additional
knockout tournament(s) where players eliminated from the first tournament can
have at least one more chance to qualify.

My vote is for the double-elimination knockout format, which was originally
suggested by Khalifman. In this scenario, losing a match does not eliminate
you from the tournament; you simply drop down to the losers' bracket, where
you keep playing elimination matches against other players who have also lost
once. You aren't eliminated until you lose one of those matches. This is an
ideal way to allow multiple players to qualify, and it lends itself to all kinds
of variations if a specific number of qualifiers is desired. Unless you've thought
a little bit about it, you may not be aware that there are many ways to structure
a double-elimination tournament. It's not as simple as a single-elimination
tournament would be, and there can be pitfalls. However, it turns out that there
are very clean ways to design a 128-player double-elimination knockout tournament
so that it generates one, two, three, four, five, six, seven, or eight people
who qualify into a championship cycle.

My favorite approach is to have all winners' bracket matches last four games
(starting with Round 3), while all losers' bracket matches last two games. This
leaves room for two rounds of losers' bracket matches to be played simultaneously
with each round of winners' bracket matches. In addition to the obvious benefit
of having longer matches among the top players, I like this approach because
it preserves the "power of two" numbers (128, 64, 16, etc.) that are
so prevalent in typical knockout tournaments. Otherwise you can easily fall
into a situation where one bracket reduces down to an odd number of players,
and you have to give one of them a late-round bye, and it's very ugly.

I know this is somewhat complicated, so I want to provide an illustrative example.
As always, we would start with 128 players, and Round 1 consists of two-game-matches.
Instead of going home, the 64 players who lose in Round 1 will drop down to
the losers' bracket, where they get to face other players who have also lost
one match. Thus, at the start of Round 2 we have 64 players in the winners'
bracket, and 64 players in the losers' bracket.

The Round 2 matches would again be two games long, and so at the end of Round
2 there would be 32 players still in the winners' bracket, and 32 players who
just dropped down from the winners' bracket to the losers' bracket, and 32 players
who just won their losers' bracket match. So now we have twice as many players
in the losers' bracket as in the winners' bracket. The key is to preserve that
2:1 ratio until the end.

To continue the example, and to show how we preserve that 2:1 ratio, let me
go through one more round. We start Round 3 with 32 undefeated players (in the
winners' bracket) and 64 players with one loss (in the losers' bracket). This
round lasts four days, rather than two. In the winners' bracket, you have the
usual 16 four-game matches involving undefeated players. Meanwhile, during the
first two days of this round, down in the losers' bracket there are 32 normal
two-game matches between players with one loss. That gets it down to 32 players
left in the losers' bracket, and those 32 players immediately play another set
of two-game matches (across days three and four of the round), getting us down
to 16 players still in the losers' bracket. At the end of the four days, there
are 16 undefeated players in the winners' bracket, 16 players who just dropped
down to the losers' bracket, and 16 players who just won the last set of losers'
bracket matches. That leaves us with 16 undefeated players in the winners' bracket,
and 32 players with one loss in the losers' bracket. As you can see, the 2:1
ratio is preserved, and subsequent rounds work the same way.

Ultimately, after Round 7, we are left with one player in the winners' bracket,
and two players in the losers' bracket. If we had wanted only one player to
qualify into the Candidates cycle, then the two players in the losers' bracket
could play each other as the only Round 8 match, and the survivor faces the
undefeated player, who gets draw odds in the Round 9 championship match. This
has the wonderful benefit that the tournament championship can't be decided
by tiebreak games (remember the FIDE Championship final between Anatoly Karpov
and Viswanathan Anand which went to a rapid tiebreak?). If we had wanted two
qualifiers, then we could simply take the undefeated player and the winner of
that Round 8 match. And if we had wanted three qualifiers, then we would have
just taken the original three players who were still around after Round 7, without
bothering about the Round 8 or Round 9 matches, unless they were needed for
prize money considerations or seeding into candidate matches.

The really neat part is that if you want a few more people to qualify, you
can control the number of qualifiers by deciding at what point you switch over
to having only one set of losers' bracket matches per round (instead of two).
By controlling which round this happens in, you can make the tournament generate
four, five, six, seven, or even eight qualifiers. This makes the double-elimination
knockout tournament perfectly suited to whatever type of championship cycle
is proposed. Presumably there would be some kind of plan where there is a series
of final matches, including the defending champion and maybe others, plus a
specific number of qualifiers from the knockout tournament.

Everyone would love to have the knockout tournament include matches of four
games, instead of two. Everyone, that is, except the sponsor, who has to support
a much longer event, and that eats up a lot of money. So, although it pains
me, I feel compelled to point out that we could do that whole format I just
described, except in half the time, by having the winners' bracket matches last
two days each, and the losers' bracket matches last ONE day each.

In fact, it really wouldn't look too different from the current Tripoli tournament.
The main difference is that the first time you lose a match, you aren't eliminated
yet. Instead, you come back tomorrow and play a single-day match against someone
else in the losers' bracket, maybe following the same time controls as a typical
tiebreak. If you win, you come back the next day and do the same thing again,
while the undefeated players are conducting their own tiebreak matches. If you
survive long enough, to the round where once again there is only one losers'
bracket match per round, then you're back to one game per day at regular time
controls, with tiebreaks every other day. It's grueling for the players, but
I'm sure they would prefer it to the current alternative of a single-elimination
tournament, where they just go home if they lose one match.

It is very easy to criticize the current knockout format and call it a lottery,
without suggesting a truly practical alternative. It needs to have the support
of the top players, and it needs to be perceived as a more effective structure
that will be won by a more deserving player. I hope you agree that my suggested
changes to the current format would be both superior and quite feasible. I also
hope that you have enjoyed my articles and my statistical analysis of the odds,
throughout the Tripoli tournament. The updated odds will continue to appear
as the tournament progresses, in the ChessBase reports at the end of each round.

Please feel free to send me email at jeff(at)chessmetrics.com if you have any
questions, comments, or suggestions.

Jeff Sonas is a statistical chess analyst who has
written dozens of articles since 1999 for several chess websites. He
has invented a new rating system and used it to generate 150 years of
historical chess ratings for thousands of players. You can explore these
ratings on his Chessmetrics
website. Jeff is also Chief Architect for Ninaza, providing web-based
medical software for clinical trials. Previous articles:

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